Hub & regenerator location and survivable network design

With the vast development of the Internet, telecommunication networks are employed in numerous different outlets. In addition to voice transmission, which is a traditional utilization, telecommunication networks are now used for transmission of different types of data. As the amount of data transmitted through the network increases, issues such as the survivability and the capacity of the network become more imperative. In this dissertation, we deal with both design and routing problems in telecommunications networks. Our first problem is a two level survivable network design problem. The topmost layer of this network consists of a backbone component where the access equipments that enable the communication of the local access networks are interconnected. The second layer connects the users on the local access network to the access equipments, and consequently to the backbone network. To achieve a survivable network, one that stays operational even under minor breakdowns, the backbone network is assumed to be 2-edge connected while local access networks are to have the star connectivity. Within the literature, such a network is referred to as a 2-edge connected/star network. Since the survivability requirements of networks may change based on the purposes they are utilized for, a variation of this problem in which local access networks are also required to be survivable is also analyzed. The survivability of the local access networks is ensured by providing two connections for every component of the local access networks to the backbone network. This architecture is known as dual homing in the literature. In this dissertation, the polyhedral analysis of the two versions of the two level survivable network design problem is presented; separation problems are analyzed; and branch-and-cut algorithms are developed to find exact solutions. The increased traffic on the telecommunications networks requires the use of high capacity components. Optical networks, composed of fiber optical cables, offer solutions with their higher bandwidths and higher transmission speeds. This makes the optical networks a good alternative to handle the rapid increase in the data traffic. However, due to signal degradation which makes signal regeneration necessary introduces the regenerator placement problem as signal regeneration is a costly process in optical networks. In the regenerator placement problem, we study a location and routing problem together on the backbone component of a given telecommunications network. Survivability is also considered in this problem simultaneously. Exact solution methodologies are developed for this problem: mathematical models and some valid inequalities are proposed; separation problems for the valid inequalities are analyzed and a branch-and-cut algorithm is devised.